Time optimal control for a nonholonomic system with state constraint

Jérome Lohéac; Jean-François Scheid

doi:10.3934/mcrf.2013.3.185

Article Contents

2013, Volume 3, Issue 2: 185-208. Doi: 10.3934/mcrf.2013.3.185

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Time optimal control for a nonholonomic system with state constraint

Jérome Lohéac^1, and
Jean-François Scheid^1,

1.
Université de Lorraine, Institut Elie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506

Received: May 31, 2012

Revised: November 30, 2012

Published: May 2013

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Abstract

The aim of this paper is to tackle the time optimal controllability of an $(n+1)$-dimensional nonholonomic integrator. In the optimal control problem we consider, the state variables are subject to a bound constraint. We give a full description of the optimal control and optimal trajectories are explicitly obtained. The optimal trajectories we construct, lie in a 2-dimensional plane and they are composed of arcs of circle.

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Mathematics Subject Classification: 49K15, 49K30, 49J15, 49J30, 37J60, 93C15.

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